If a, b, c and d are integers, is (2a·3b)/(2c·3d) even? (

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If a, b, c and d are integers, is (2a·3b)/(2c·3d) even?

(1) a>c

(2) b=c+d

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by Brent@GMATPrepNow » Mon Jan 14, 2013 11:03 am
varun289 wrote:If a, b, c and d are integers, is (2a·3b)/(2c·3d) even?

(1) a>c

(2) b=c+d
Target question: Is (2a·3b)/(2c·3d) even?

We can simplify this expression.
(2a·3b)/(2c·3d) = 6ab/6cd = ab/cd

Rephrased target question: Is ab/cd even?

Statement 1: a>c
There are several sets of numbers that meet this condition. Here are two:
Case a: a=4, b=4, c=2 and d=2, in which case ab/cd is even
Case b: a=3, b=4, c=2 and d=2, in which case ab/cd is not even
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: b=c+d
There are several sets of numbers that meet this condition. Here are two:
Case a: a=4, b=4, c=2 and d=2, in which case ab/cd is even
Case b: a=3, b=4, c=2 and d=2, in which case ab/cd is not even
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
There are still several sets of numbers that meet this condition. Here are two:
Case a: a=4, b=4, c=2 and d=2, in which case ab/cd is even
Case b: a=3, b=4, c=2 and d=2, in which case ab/cd is not even
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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